//https://leetcode.cn/problems/interleaving-string/

class Solution {
public:
    bool isInterleave(string s1, string s2, string s3) {
        int n = s1.size(), m = s2.size();

        if (n + m != s3.size()) return false;

        vector<vector<bool>> dp(n + 1, vector<bool>(m + 1));
        s1 = " " + s1; s2 = " " + s2; s3 = " " + s3;
        dp[0][0] = true;
        for (int j = 1; j <= m; j++)
        {
            if (s2[j] == s3[j]) dp[0][j] = true;
            else break;
        }

        for (int i = 1; i <= n; i++)
        {
            if (s1[i] == s3[i]) dp[i][0] = true;
            else break;
        }

        for (int i = 1; i <= n; i++)
        {
            for (int j = 1; j <= m; j++)
            {
                dp[i][j] = (s1[i] == s3[i + j] && dp[i - 1][j]) ||
                    (s2[j] == s3[i + j] && dp[i][j - 1]);
            }
        }

        return dp[n][m];

    }
};